Matching Tag: polynomial-progressions
Let P 1 , … , P m ∈ Z [ y ] P_1,\dots,P_m\in\mathbf{Z}[y] P 1 , … , P m ∈ Z [ y ] 0 ≤ i ≤ m 0\leq i\leq m 0 ≤ i ≤ m
Let P 1 , … , P s ∈ Z [ x ] P_1,\dots,P_s\in\mathbb{Z}[x] P 1 , … , P s ∈ Z [ x ] ω ∈ { 0 , 1 } s \omega\in\{0,1\}^s ω ∈ { 0 , 1 } s ω = ( ω 1 , … , ω s ) \omega=(\omega_1,\dots,\omega_s) ω = ( ω 1 , … , ω s )
Let P 1 , … , P s ∈ Z [ x ] P_1,\dots,P_s\in\mathbb{Z}[x] P 1 , … , P s ∈ Z [ x ] f ω : Z / N Z → C f_\omega:\mathbb{Z}/N\mathbb{Z}\to\mathbb{C} f ω : Z / N Z → C
Let P 1 , … , P s ∈ Z [ x ] P_1,\dots,P_s\in\mathbb{Z}[x] P 1 , … , P s ∈ Z [ x ] f ω : Z / N Z → C f_\omega:\mathbb{Z}/N\mathbb{Z}\to\mathbb{C} f ω : Z / N Z → C
Let t ∈ N + t\in\mathbb{N}_+ t ∈ N + P ⃗ ∈ R [ x , y ] t + 1 \vec{P}\in\mathbb{R}[x,y]^{t+1} P ∈ R [ x , y ] t + 1 0 ⩽ i ⩽ t 0\leqslant i\leqslant t 0 ⩽ i ⩽ t H K i ( P ⃗ ) \mathcal{HK}_i(\vec{P}) H K i ( P )
